Problem: Solve for $x$ and $y$ using elimination. ${x-3y = -13}$ ${-x-5y = -35}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-8y = -48$ $\dfrac{-8y}{{-8}} = \dfrac{-48}{{-8}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {x-3y = -13}\thinspace$ to find $x$ ${x - 3}{(6)}{= -13}$ $x-18 = -13$ $x-18{+18} = -13{+18}$ ${x = 5}$ You can also plug ${y = 6}$ into $\thinspace {-x-5y = -35}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(6)}{= -35}$ ${x = 5}$